Spectral Analysis for Univariate Time Series

Donald B. Percival, Andrew T. Walden

• Publisher: Cambridge University Press
• Year: 2020
• Print ISBN: 9781107028142
• eBook ISBN: 9781108776172
• Topic: Mathematics
• Subtopic: Probability & Statistics
• Index: Mathematics

Spectral analysis is widely used to interpret time series collected in diverse areas. This book covers the statistical theory behind spectral analysis and provides data analysts with the tools needed to transition theory into practice. Actual time series from oceanography, metrology, atmospheric science and other areas are used in running examples throughout, to allow clear comparison of how the various methods address questions of interest. All major nonparametric and parametric spectral analysis techniques are discussed, with emphasis on the multitaper method, both in its original formulation involving Slepian tapers and in a popular alternative using sinusoidal tapers. The authors take a unified approach to quantifying the bandwidth of different nonparametric spectral estimates. An extensive set of exercises allows readers to test their understanding of theory and practical analysis. The time series used as examples and R language code for recreating the analyses of the series are available from the book's website.

Table of contents

• Cover
• Half-title
• Series information
• Title page
• Copyright information
• Dedication
• Contents
• Preface
• Conventions and Notation
• Data, Software and Ancillary Material
• 1 Introduction to Spectral Analysis
• 2 Stationary Stochastic Processes
• 3 Deterministic Spectral Analysis
• 4 Foundations for Stochastic Spectral Analysis
• 5 Linear Time-Invariant Filters
• 6 Periodogram and Other Direct Spectral Estimators
• 7 Lag Window Spectral Estimators
• 8 Combining Direct Spectral Estimators
• 9 Parametric Spectral Estimators
• 10 Harmonic Analysis
• 11 Simulation of Time Series
• References
• Author Index
• Subject Index